Thumbnails are only created when a picture is uploaded to a Picture Library, as during the process of uploading, thumbnail versions of the pictures are added to a hidden
_t-folder located by the Picture Library. This is a feature associated with the built-in Picture Library, which is all but simple to be done for other library/folder types. In addition, this possibly isn't doable at all in SharePoint Online.
There's a lengthy article detailing the technical background of thumbnail and how it could be done from the scratch for SharePoint's previous version(s): Need a Thumbnail Field in the Document library for the uploaded picture… Then read this post.
My knowledge might be outdated, but I think you won't receive thumbnails of the pictures even if you re-add the pictures to the child folders. Therefore your best bet would be to add the thumbnail referred from the source it was originally stored at. To do so, you'd need to inspect the elements of the thumbnails in your source-location (i.e. the location from where you are about to move the pictures), get the URL for the thumbnail, and finally use it at your destination folder's thumbnail-column.